A combined likelihood ratio/information ratio bootstrap technique for estimating the number of components in finite mixtures

Modified MIR is a Monte-Carlo algorithm used for bootstrapping minimum information ratios in order to assess the number of unknown components in finite mixtures. The method was proposed as a modification of the minimum information ratio (MIR) method, and was proved to outperform it. Further simulations and a comparison with some other approaches confirm that the method works well for reasonable sample sizes. However, an important drawback which occurs with information ratio driven methods is that they do not allow for testing for the hypothesis of a single-component model. In order to overcome this problem, a combined method is proposed which consists of including a bootstrap likelihood ratio step and a modified MIR step into a single programming package. The bootstrap likelihood ratio methods show in general nice performances, so the combined method is also expected to be adequate for detecting single-component models. This, in turn, implies that the performance of the method is expected to be very similar to that of modified MIR in situations where the model is a true mixture. A simulation exercise is carried out, which confirms this feeling. This result is then in support of using the combined method rather than modified MIR for practical applications.